EP3043148B1 - Cap pour une solution de navigation hybride sur la base de mesures étalonnées magnétiquement - Google Patents

Cap pour une solution de navigation hybride sur la base de mesures étalonnées magnétiquement Download PDF

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EP3043148B1
EP3043148B1 EP15193083.1A EP15193083A EP3043148B1 EP 3043148 B1 EP3043148 B1 EP 3043148B1 EP 15193083 A EP15193083 A EP 15193083A EP 3043148 B1 EP3043148 B1 EP 3043148B1
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heading
magnetic
filter
estimate
solution
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EP3043148A1 (fr
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Zdenek Kana
Jindrich Dunik
Milos SOTAK
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Honeywell International Inc
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Honeywell International Inc
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
    • G01S19/42—Determining position
    • G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
    • G01S19/47—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being an inertial measurement, e.g. tightly coupled inertial
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/04—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by terrestrial means
    • G01C21/08—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by terrestrial means involving use of the magnetic field of the earth
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • G01C21/1654—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments with electromagnetic compass
    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B44/00—Automatic control systems specially adapted for drilling operations, i.e. self-operating systems which function to carry out or modify a drilling operation without intervention of a human operator, e.g. computer-controlled drilling systems; Systems specially adapted for monitoring a plurality of drilling variables or conditions
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C17/00—Compasses; Devices for ascertaining true or magnetic north for navigation or surveying purposes
    • G01C17/38—Testing, calibrating, or compensating of compasses

Definitions

  • European patent application, publication number EP2264485A1 discloses a method for determining a continuous trajectory of a moving object from a DGPS data set.
  • PCT patent application, publication number WO2014022664A2 discloses a method and apparatus of integrating a three-axis magnetometer and a three-axis accelerometer to provide attitude and heading.
  • US patent application, publication number US2012265440A1 discloses a navigation system comprises a satellite navigation receiver and an inertial measurement unit, and employing a Kalman filter.
  • the present invention provides for a method for determining a heading for a hybrid navigation system with magnetometer aiding and a corresponding system as claimed in the accompanying claims.
  • Embodiments described herein provide a heading solution based on three-dimensional magnetometer measurements with a proper modeling and treating of the errors in the magnetometer measurements, while ensuring the three-dimensional magnetometer measurements do not affect the roll or pitch solutions.
  • Embodiments described herein also provide a global navigation satellite system (GNSS) signal in space integrity for navigation parameters including the heading based on solution separation without a significant increase in computational demands.
  • GNSS global navigation satellite system
  • Figure 1 depicts one exemplary embodiment of an object 12 with one or more inertial measurement units (IMUs) 30 including one or more gyroscopes 32 and accelerometers 34.
  • Object 12 also includes one or more GNSS receivers 14 that receive signals from a number of satellites 1-N.
  • Object 12 also includes one or more magnetometers 10.
  • Object 12 can also optionally include one or more other sensors 11, such as one or more barometers.
  • Object 12 further includes one or more processing devices 16 coupled to one or more memory units 18 that store instructions (e.g., software) as well as data received from the GNSS receiver(s) 14, the magnetometer(s) 10, the IMU(s) 30, and the optional other sensor(s) 11.
  • instructions e.g., software
  • the instructions, when executed on the processing device(s) 16, are configured to cause the processing device(s) 16 to determine a hybrid navigation solution for the object 12 based on the data from the GNSS receiver(s) 14, the magnetometer(s) 10, and IMU(s) 30.
  • the instructions on the memory 18 can include a main navigation filter module 20, a sub-solution module 22, a magnetic calibration filter module 24, and a navigation solution integrity module 26 that are configured to implement their respective functions on the processing device(s) 16. It should be understood that the demarcation of the modules 20, 22, 24, 26 described herein is an example, and in other examples, more, fewer, and/or different modules can be used, and the actions assigned to a given module may be different.
  • the object 12 can include any object for which it is desired to determine a navigation solution, such as a manned or unmanned vehicle (e.g., aircraft, boat, car).
  • a navigation solution determined by the processing device(s) 16 can be output to a navigation management system 40 that includes another processing device(s) to oversee navigation and provide commands to various units, for example, the sensor(s) 30, GNSS receiver(s) 14, and processing device(s) 16.
  • the navigation management system 40 could be a Flight Management System that communicates with a pilot and a ground control station through display monitors or printers.
  • processing device(s) 16 and the navigation management system 40 may be combined in a single unit.
  • the navigation management system 40 can be implemented using any suitable processing device(s) and display technology such as, but not limited to, printers, computer screens, various CRT, active and passive matrix LCD, and plasma display units.
  • the processing device(s) 16 and the processing device(s) in the navigation management system 40 may include any suitable processing device(s) such as a digital signal processing device (DSP), central processing unit (CPU), micro-controller, or arithmetic logic unit.
  • Memory 18 may comprise any suitable storage entity such as a flash drive, magnetic-disk drive, RAM (e.g., DRAM), ROM, PROM, or CD/DVD/Blu-ray, optical storage or optoelectronics circuits.
  • the IMU(s) 30, GNSS receiver(s) 14, the magnetometer(s) 10, and the optional other sensor(s) 11 can all be physically attached to the object 12, such that their measurements correspond to the object 12. Accordingly, the IMU(s) 30 can be configured to sense inertial movement of the object 12 about three mutually orthogonal axes to obtain three-dimensional inertial measurements corresponding to the object 12.
  • the GNSS receiver(s) 14 can be configured to receive signals at the location of the object 12 from the GNSS satellites 1-N, and to provide pseudorange measurements to the processing device(s) 16 based on the received signals.
  • Example GNSS satellite constellations include the global position system (GPS), GLONASS, Galileo, and Beidou constellations.
  • the magnetometer(s) 10 can be configured to sense Earth's magnetic field in three mutually orthogonal directions at the location of the object 12 to obtain three-dimensional magnetic measurements corresponding to the object 12.
  • the optional sensor(s) 11 include one or more barometers configured to sense a barometric pressure at the location of the object to obtain barometric measurements corresponding to the object.
  • Figure 2 illustrates one embodiment of a method 200 for determining a navigation solution using the system described with respect to Figure 1 .
  • Signals from a plurality of GNSS satellites are received at the location of the object 12 by the GNSS receiver(s) 14.
  • the GNSS receiver(s) 14 can then generate pseudorange measurements based on the received signals (block 202).
  • Three-dimensional (3-D) inertial measurements corresponding to the object 12 are obtained with the IMU(s) 30 (block 202).
  • 3-D magnetic measurements corresponding to the object 12 are obtained with the magnetometer(s) 10 (block 202).
  • any optional sensor(s) 11 e.g., one or more barometers
  • measurements corresponding to the object 12 e.g., barometric measurements
  • the pseudorange measurements, 3-D inertial measurements, 3-D magnetic measurements, and the measurements from the optional other sensor(s) 11 e.g., barometric measurements
  • the processing device(s) 16 are provided to the processing device(s) 16.
  • the processing device(s) 16 can execute the instructions on the memory 18 to perform the following actions based on the pseudorange measurements, 3-D inertial estimates, 3-D magnetic measurements, and barometric measurements (if present).
  • the instructions on the memory 18 include magnetic calibration filter module 24, which cause the processing device(s) 16 to maintain a magnetic calibration filter (block 204) as described below based on the pseudorange measurements, 3-D inertial measurements, 3-D magnetic measurements and the measurements from the optional sensor(s) 11 (if present).
  • FIG. 3 is a block diagram illustrating the magnetic calibration filter 302, other filters implemented by the processing device(s) 16, and the interaction amongst the filters and with the IMU(s) 30, GNSS receiver(s) 14, magnetometer(s) 10, and optional sensor 11 (e.g., a barometer).
  • the magnetic calibration filter 302 (also referred to herein as simply "calibration filter 302") is configured to estimate components of a state vector corresponding to the object 12 and can be based on an estimation algorithm following the Kalman filter design approach.
  • the state vector components can include states for position, velocity, roll, pitch, and heading of the object 12. In an example, these states include nine or ten states for 3-D position and velocity as well as roll, pitch, and heading of the object 12.
  • the state vector components can include states for calibration of the 3-D inertial measurements. In an example, these states include six states for calibration of 3-D acceleration and angular rate.
  • the state vector components can include states for bias and drift of the clock(s) of the GNSS receiver(s) 14, and states for pseudorange biases of the signals received by the GNSS receiver(s) 14.
  • the calibration filter 302 can also estimate a state for bias of the barometric measurement. Manners of implementing all of these states are known to those skilled in the art.
  • the state vector components can also include states for bias of the 3-D magnetic measurements.
  • the states for bias of the 3-D magnetic measurements include nine states for soft iron biases about the 3-D axes and three states for hard iron biases about the 3-D axes. Manners of implementing such states for bias of the 3-D magnetic measurements are known to those skilled in the art.
  • the calibration filter 302 operates recursively to iteratively update the state vector based on updated inertial measurements, pseudorange measurements, magnetic measurements, and barometric measurements (if present).
  • the calibration filter 302 can use the inertial measurements for a prediction step, and the pseudorange measurements, the magnetic measurements, and the barometric measurements (if present) to update the state vector from the prediction step in the filtering step.
  • an "artificial heading” is generated (block 206 of Figure 2 ) for aiding of a main navigation filter 304 (also referred to herein as simply "main filter 304").
  • the term artificial heading is defined for the sake of simplicity as this heading calculation aids the main filter 304 with a magnetic measurement that is calibrated and is limited to heading only; the magnetic measurement does not affect pitch or roll.
  • the artificial heading can be a magnetic measurement that is calibrated for hard and soft iron bias and compensated for declination and inclination.
  • the main filter 304 can estimate a main navigation solution including a heading, pitch, and roll with the benefit of calibrated magnetic measurements for the heading, and while ensuring that the pitch and roll are unaffected by the magnetic measurements.
  • the artificial heading is based on the 3-D magnetic measurements, roll and pitch estimates of the object from the main filter 304, and a magnetic declination based on a position estimate of the object from the main filter 304.
  • the artificial heading uses the biases given by the magnetic bias states from the calibration filter 302 and adjusts the magnetic measurements from the magnetometer(s) 10 based thereon to calibrate the magnetic measurements. Since the calibration filter 304 takes in 3-D magnetic measurements and estimates 3-D hard iron biases and 3-D soft iron biases, the magnetic measurements can be fully calibrated.
  • the calibrated magnetic measurements are calculated in the body frame of the object 12, as denoted above by the superscript 'B' .
  • the calculation to determine the artificial heading reduces the 3-D magnetic measurements down to a one-dimensional heading only value, thus removing any magnetic measurements about the pitch and roll axis. Accordingly, the calibrated magnetic measurements can then be transformed based on the roll and pitch estimates from the main filter 304 and the magnetic declination at the position estimated by the main filter 304 to arrive at the artificial heading.
  • ⁇ is the roll estimate from the main navigation filter 304
  • ⁇ is the pitch estimate from the main navigation filter 304
  • ⁇ dec is the magnetic declination
  • m cal Bz are calibrated magnetic measurements with components x, y, and z the body frame, respectively.
  • the main filter module 20 is configured to cause the processing device(s) 16 to calculate the artificial heading, but in other examples other modules can cause the calculation.
  • the artificial heading is processed by the main filter 304 as a measurement. Similar to the calibration filter 302, the main filter 304 can use the 3-D inertial measurements for a prediction step. Instead of using the 3-D magnetic measurements as the calibration filter 302 does, however, the main filter 304 uses the artificial heading along with the pseudorange measurements and (if present) measurements from the optional other sensor(s) 11 (e.g., barometer) to update the prediction step in the filtering step.
  • the optional other sensor(s) 11 e.g., barometer
  • the main filter module 20 is configured to cause the processing device(s) 16 to model the error in the artificial heading, ⁇ ma , as time correlated heading bias error, b ⁇ ,ma , plus uncorrelated ("white") noise, w ma .
  • the time correlated heading bias error, b ⁇ ,ma is modeled as a state in the state space of the main filter 304.
  • the main filter 304 uses statistics from the calibration filter 302 to estimate the state for time correlated bias. In particular, the statistics of time correlated bias can be calculated based on the statistics of magnetic bias state estimates from the calibration filter 302 and a magnetic declination error effect at a position of the object estimated by the main filter 304.
  • these statistics can be transformed on the bias statistics with the usage of first order Taylor series expansion.
  • b ⁇ is the time correlated bias
  • ⁇ ⁇ is the time constant of the GM process
  • w GM uncorrelated white noise driving the GM process.
  • the subscript 'ma' denotes that the respective value is from/part of the main filter 304.
  • the main filter module 20 is configured to cause the processing device(s) 16 to estimate a main navigation solution for the object 12 (block 208 of Figure 2 ).
  • the main filter 304 estimating the main navigation solution includes estimating states for position, velocity, roll, pitch, and heading of the object 12. In an implementation, these states include nine or ten states for 3-D position and velocity as well as roll, pitch, and heading of the object 12. Estimating the main navigation solution can also include estimating states for calibration of the 3-D inertial measurements. In an example, these states include six states for calibration of 3-D acceleration and angular rate.
  • the main filter 304 can also estimate states for bias and drift of the clock(s) of the GNSS receiver(s) 14, a state for barometer bias (if a barometer is present), and states for pseudorange biases for the signals received by the GNSS receiver(s) 14.
  • the main filter 304 operates recursively to iteratively update the states based on updated inertial measurements, pseudorange measurements, barometric measurements (if present), and artificial heading, and can be based on an estimation algorithm following the Kalman filter design approach.
  • the main navigation solution can be output to a navigation management system 40, which can take appropriate action such as controlling operation of the object 12 based on the main navigation solution.
  • the system of Figure 1 can also be configured to provide integrity on the main navigation solution.
  • This integrity can be provided using a solution separation technique.
  • Solution separation techniques involve maintaining a plurality of sub-solutions for the main navigation solution by a plurality of sub-filters 306-1 through 306-N (block 210 of Figure 2 ).
  • a separate sub-solution is maintained for each set of N-1 satellites, where the main navigation solution incorporates measurements from all N satellites.
  • each sub-solution incorporates measurements from a different combination of N-1 satellites. That is, sub-filter 306-n excludes measurements from satellite n. If a satellite has large errors, it will drive one or more of the sub-solutions away from the main navigation solution maintained by the main filter 304. More specifically, there are solution differences (also referred to herein as "separations") between the main navigation solution of the main filter 304 and each sub-solution of each sub-filter 306.
  • the sub-solution module 22 is configured to cause the processing device(s) 16 to calculate such sub-solutions for the main navigation solution.
  • each sub-filter 306 estimates generally the same state vector as the main filter 304. That is, the meaning of the state variables between the sub-solutions and the main solution are the same; however, the state vectors of some of the sub-solutions might be of a different dimension than the state vector of the main solution. Since a sub-solution processes N-1 measurements, there will be just N-1 pseudorange biases estimated (in contrast to the N biases in the main filter). Generally, however, in examples where the main filter estimates states for 3-D position, 3-D velocity, roll, pitch, and heading, the sub-solutions can estimate states for the same.
  • the sub-filters 306 also estimate the states for calibration of the 3-D inertial measurements, bias and drift of the clock(s) of the GNSS receiver(s) 14, a state for barometer bias (if a barometer is present), and pseudorange biases for the signals received by the GNSS receiver(s) 14. Each sub-filter 306 can also estimate a state for time correlated bias of the artificial heading.
  • the sub-filters 306 can estimate these states based on the 3-D inertial measurements, the pseudorange measurements from the GNSS receiver(s) 14, and an artificial heading based on the calculations analogous to those used in the calibration filter 302.
  • the same artificial heading that was used for the main filter 304 can be used for each of the sub-filters 306.
  • the artificial heading used by each sub-filter can be based on the roll and pitch estimates from the respective sub-filter 306 and the magnetic declination at the position estimated by that respective sub-filter 306. Accordingly, each sub-filter can use an independent artificial heading that is calculated by transforming the calibration magnetic measurements based on the roll, pitch, and position of the respective sub-filter.
  • the navigation solution integrity module 26 is configured to cause the processing device(s) 16 to determine protection limits based on the main navigation solution and the sub-solutions. Manners of determining a protection limit (the integrity) from the state vectors maintained by the main filter 304 and sub-filters 306 for navigation values other than heading are known to those skilled in the art based on the separations between the main navigation solution and each respective sub-solution for the respective navigation values.
  • the heading protection limit is calculated based on the heading estimate from the calibration filter 302. In an example, however, sub-solutions of the heading estimate from the calibration filter are not calculated in order to reduce the amount of computation required. Instead, covariances for hypothetical sub-solution heading estimates of the calibration filter 302 are approximated (block 212 of Figure 2 ).
  • the covariances for hypothetical sub-solution heading estimates (also referred to herein as "sub-solution heading covariances") of the calibration filter 302 can be approximated based on the ratio of heading covariances of the main filter 304, each of its respective sub-filters 306, and the calibration filter 302. In particular, it can be assumed that the ratio between the heading covariance of the calibration filter 302 and the heading covariance of a respective ('n') hypothetical sub-filter for the calibration filter 302 is approximately equal to the ratio between the heading covariance of the main filter 304 and the heading covariance of its corresponding 'n' sub-filter 306.
  • each sub-solution heading covariance for the calibration filter 302 can be calculated according to Cov ⁇ n , 3 ⁇ D ⁇ ⁇ ovrb 2 Cov ⁇ n , 3 ⁇ D Cov ⁇ 0 , DMHA Cov ⁇ n , DMHA where Cov( ⁇ ) n,3-D is the sub-solution heading covariance for the hypothetical sub-solution 'n' of the calibration filter 302, ⁇ ovrb is the overbounding factor that is greater than or equal to 1, Cov( ⁇ ) 0,3-D is the heading covariance of the calibration filter 302, Cov( ⁇ ) 0,DMHA is the heading covariance of the main filter 304, and Cov( ⁇ ) n,DMHA is the heading covariance of sub-solution 'n' from
  • the heading protection limit along with protection limits for the other navigation values can be provided to the navigation management system 40.
  • the navigation management system 40 can then take appropriate action such as initiating an alarm if a protection limit is out of range.
  • this method can be used to provide integrity for the magnetically aided heading solution with only one additional filter (the magnetic calibration filter 302) more than a conventional solution separation implementation.
  • the above methods can be implemented with N+2 filters if fault detection, but not exclusion is implemented, where N represent the number of processes pseudorange measurements.
  • the above methods represent suitable navigation solutions for all navigation systems using low-cost inertial sensor (typically MEMS based) aided by GNSS and magnetometer.
  • Such systems can, for example, be referred to as GPS/INS, GNSS/INS, GPS/AHRS, GNSS/AHRS, and GPAHRS.
  • the subject matter described herein can be used in the advanced receiver monitoring integrity method (ARAIM) or any other method based on the solution separation, such as a solution separation method where N represents a number of fault states to be mitigated, rather than the number of pseudorange measurements.
  • ARAIM advanced receiver monitoring integrity method
  • the one or more GNSS receivers 14 include multiple GNSS antennas to receive GNSS signal and can provide calculated values for the attitude and heading of the aircraft using GNSS interferometry.
  • GNSS errors contribute directly to the sources of errors for attitude and heading.
  • the GNSS receiver(s) 14 can compute a snapshot least squares solution using only the multiple GNSS measurements.
  • a hybrid solution can be calculated by processing the GNSS-derived attitude and heading solutions as measurements to the filter.
  • the above solution separation and Kalman filter techniques are applicable to multiple antennas and sets of data in determining the errors in the estimates of attitude and heading.
  • solution separation technique discussed above corresponds to GNSS; and the same technique can be carried over to the multiple sets of data from other instruments.

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Claims (10)

  1. Procédé (200) de détermination d'un cap pour un système de navigation hybride à l'aide de magnétomètres, le procédé comprenant les étapes suivantes :
    réception de signaux (202) en provenance d'une pluralité de satellites d'un système mondial de satellites de navigation (GNSS) en un emplacement correspondant à un objet ;
    obtention de mesures inertielles tridimensionnelles (202) auprès d'un ou de plusieurs capteurs inertiels correspondant à l'objet ;
    obtention de mesures magnétiques tridimensionnelles (202) auprès d'un ou de plusieurs magnétomètres correspondant à l'objet ;
    estimation d'états (204) pour la position, la vitesse, le roulis, le tangage et le cap de l'objet à l'aide d'un filtre d'étalonnage magnétique ;
    estimation d'états (204) pour l'étalonnage des mesures inertielles tridimensionnelles à l'aide du filtre d'étalonnage magnétique ;
    estimation d'états (204) pour la dérive et le biais d'une horloge GNSS à l'aide du filtre d'étalonnage magnétique ; et
    estimation d'états (204) pour des biais de pseudodistance pour les signaux en provenance des satellites GNSS à l'aide du filtre d'étalonnage magnétique ;
    estimation de neuf états de biais du fer doux et de trois états de biais du fer dur (204) pour des biais des mesures magnétiques tridimensionnelles à l'aide du filtre d'étalonnage magnétique à partir des mesures inertielles tridimensionnelles, de données issues des signaux en provenance de la pluralité de satellites GNSS et des mesures magnétiques tridimensionnelles ;
    calcul d'une estimation de cap étalonnée (206) pour l'objet sous la forme ψ ma = atan − m cal Bz sin φ + m cal By cos φ m cal Bx cos θ + m cal By sin θ sin φ + m cal Bz sin θ cos φ − ψ dec
    Figure imgb0063
     où φ représente l'estimation de roulis issue du filtre de navigation principal, θ représente l'estimation de tangage issue du filtre de navigation principal, ψdec représente la déclinaison magnétique, et m cal Bx ,
    Figure imgb0064
     m cal By
    Figure imgb0065
     et m cal Bz
    Figure imgb0066
     représentent des mesures magnétiques étalonnées de composantes respectives x, y et z dans le repère corps, m cal B
    Figure imgb0067
     étant calculée sous la forme m cal B = D mag − 1 m ˜ B − b mag B ,
    Figure imgb0068
     où D mag représente la matrice d'états de biais magnétiques correspondant à des biais du fer doux, b mag B
    Figure imgb0069
     représente le vecteur d'états de biais magnétiques correspondant à des biais du fer dur, et m̃ B représente les mesures magnétiques tridimensionnelles ;
    estimation d'une solution de navigation principale (208) pour l'objet à l'aide d'un filtre de navigation principal à partir des mesures inertielles tridimensionnelles, de données issues des signaux en provenance d'une pluralité de satellites GPS et de l'estimation de cap étalonnée.
  2. Procédé selon la revendication 1, comprenant les étapes suivantes :
    estimation d'états (208) pour l'étalonnage des mesures inertielles tridimensionnelles à l'aide du filtre de navigation principal ;
    estimation d'états (208) pour l'étalonnage d'une horloge GNSS à l'aide du filtre de navigation principal ; et
    estimation d'états (208) pour des biais de pseudodistance pour les signaux en provenance des satellites GNSS à l'aide du filtre de navigation principal,
    l'étape d'estimation d'une solution de navigation principale (208) comportant l'étape d'estimation d'états pour la position, la vitesse, le roulis, le tangage et le cap de l'objet.
  3. Procédé selon l'une quelconque des revendications 1 et 2, comprenant l'étape suivante :
    estimation d'une erreur de biais de cap corrélé temporellement (208) de l'estimation de cap étalonnée à l'aide du filtre de navigation principal, ses statistiques étant approximées en fonction de statistiques des états de biais magnétiques de l'objet issus du filtre d'étalonnage magnétique et de statistiques de la déclinaison magnétique fonction de statistiques d'estimation de position de l'objet issues du filtre de navigation principal.
  4. Procédé selon l'une quelconque des revendications 1 à 3, comprenant l'étape suivante :
    estimation de statistiques de bruit non corrélé (208) de l'estimation de cap étalonnée en fonction de statistiques de bruit de mesure des magnétomètres et de statistiques de l'effet d'une erreur d'attitude sur l'estimation de cap étalonnée.
  5. Procédé selon l'une quelconque des revendications 1 à 4, comprend les étapes suivantes :
    estimation d'une pluralité de sous-solutions (210) pour la solution de navigation principale à l'aide d'une pluralité de sous-filtres à partir d'une séparation de solution ;
    calcul d'une covariance de cap pour chacune de la pluralité de sous-solutions ;
    calcul d'une covariance de cap pour la solution de navigation principale ;
    calcul d'une covariance de cap pour le filtre d'étalonnage magnétique ;
    approximation d'une pluralité de covariances de cap de sous-solution (212) correspondant au filtre d'étalonnage magnétique en fonction de la covariance de cap pour la solution de navigation principale, de la covariance de cap pour chacune de la pluralité de sous-solutions et de la covariance de cap pour le filtre d'étalonnage magnétique ; et
    détermination d'une limite de protection (214) qui borne l'erreur sur un cap de la solution de navigation principale en fonction de séparations respectives entre la covariance de cap pour le filtre d'étalonnage magnétique et chacune des covariances de cap de sous-solution correspondant au filtre d'étalonnage magnétique.
  6. Procédé selon la revendication 5, dans lequel l'étape d'approximation de la pluralité de covariances de cap de sous-solution (212) correspondant au filtre d'étalonnage magnétique comporte l'étape d'approximation de la covariance de cap de sous-solution n, Cov(ψ) n,3-D, selon Cov ψ n , 3 − D ≈ γ ovrb 2 Cov ψ n , 3 − D Cov ψ 0 , DMHA Cov ψ n , DMHA
    Figure imgb0070
     où γovrb représente un facteur de bornage conservateur supérieur ou égal à un, Cov(ψ) 0,3-D représente la covariance de cap du filtre d'étalonnage magnétique, Cov(ψ) 0,DMHA représente la covariance de cap du filtre de navigation principal et Cov(ψ) n,DMHA représente la covariance de cap de la sous-solution n pour le filtre de navigation principal.
  7. Système de navigation pour un objet (12), comprenant :
    un ou plusieurs dispositifs de traitement (16) ;
    un ou plusieurs récepteurs (14) d'un système mondial de satellites de navigation (GNSS), couplés au ou aux dispositifs de traitement (16), le ou les récepteurs (14) GNSS étant configurés pour obtenir des mesures de pseudodistance correspondant à un emplacement de l'objet (12) ;
    une ou plusieurs unités de mesure inertielles (IMU) (30) couplées au ou aux dispositifs de traitement (16), la ou les IMU (30) étant configurées pour obtenir des mesures inertielles tridimensionnelles correspondant à l'objet (12) ;
    un ou plusieurs magnétomètres (10) couplés au ou aux dispositifs de traitement (16), le ou les magnétomètres (10) étant configurés pour obtenir des mesures magnétiques tridimensionnelles du champ magnétique en un emplacement de l'objet (12) ; et
    un ou plusieurs dispositifs de mémoire (18) couplés au ou aux dispositifs de traitement (16) et comportant des instructions (20, 22, 24, 26) dont l'exécution par le ou les dispositifs de traitement (16) amène le ou les dispositifs de traitement (16) à :
    estimer des états (204) pour la position, la vitesse, le roulis, le tangage et le cap de l'objet à l'aide d'un filtre d'étalonnage magnétique ;
    estimer des états (204) pour l'étalonnage des mesures inertielles tridimensionnelles à l'aide du filtre d'étalonnage magnétique ;
    estimer des états (204) pour l'étalonnage d'une horloge GNSS à l'aide du filtre d'étalonnage magnétique ; et
    estimer des états (204) pour des biais de pseudodistance pour les signaux en provenance des satellites GNSS à l'aide du filtre d'étalonnage magnétique ;
    estimer neuf états de biais du fer doux et trois états de biais du fer dur pour des biais des mesures magnétiques tridimensionnelles à l'aide du filtre d'étalonnage magnétique à partir des mesures inertielles tridimensionnelles pour une étape de prédiction, et à partir de données issues du ou des récepteurs GNSS et des mesures magnétiques tridimensionnelles sous forme d'un vecteur de mesures ;
    calculer une estimation de cap étalonnée pour l'objet (12) sous la forme ψ ma = atan − m cal Bz sin φ + m cal By cos φ m cal Bx cos θ + m cal By sin θ sin φ + m cal Bz sin θ cos φ − ψ dec
    Figure imgb0071
     où φ représente l'estimation de roulis issue du filtre de navigation principal, θ représente l'estimation de tangage issue du filtre de navigation principal, ψdec représente la déclinaison magnétique, et m cal Bx ,
    Figure imgb0072
     m cal By
    Figure imgb0073
     et m cal Bz
    Figure imgb0074
     représentent des mesures magnétiques étalonnées de composantes respectives x, y et z dans le repère corps, m cal B
    Figure imgb0075
     étant calculée sous la forme m cal B = D mag − 1 m ˜ B − b mag B ,
    Figure imgb0076
     où D mag représente la matrice d'états de biais magnétiques correspondant à des biais du fer doux, b mag B
    Figure imgb0077
     représente le vecteur d'états de biais magnétiques correspondant à des biais du fer dur, et m̃ B représente les mesures magnétiques tridimensionnelles ; et
    estimer une solution de navigation principale pour l'objet (12) à l'aide d'un filtre de navigation principal à partir des mesures inertielles tridimensionnelles pour une étape de prédiction, et à partir de données issues du ou des récepteurs GNSS et de l'estimation de cap étalonnée sous forme d'un vecteur de mesures.
  8. Système selon la revendication 7, dans lequel le ou les dispositifs de traitement sont configurés pour :
    estimer des états (208) pour l'étalonnage des mesures inertielles tridimensionnelles à l'aide du filtre de navigation principal ;
    estimer des états (208) pour l'étalonnage d'une horloge GNSS à l'aide du filtre de navigation principal ; et
    estimer des états (208) pour des biais de pseudodistance pour les signaux en provenance des satellites GNSS à l'aide du filtre de navigation principal,
    l'estimation de la solution de navigation principale (208) comportant l'estimation d'états pour la position, la vitesse, le roulis, le tangage et le cap de l'objet ;
    estimer un biais d'erreur de cap corrélé temporellement de l'estimation de cap étalonnée sous la forme d'un biais (208) de l'estimation de cap étalonnée à l'aide du filtre de navigation principal, ses statistiques étant approximées en fonction de statistiques des états de biais magnétiques de l'objet issus du filtre d'étalonnage magnétique et de statistiques de la déclinaison magnétique fonction de statistiques d'estimation de position de l'objet issues du filtre de navigation principal ; et
    estimer un bruit non corrélé (208) de l'estimation de cap étalonnée en fonction de statistiques de bruit de mesure des magnétomètres et de statistiques de l'effet d'une erreur d'attitude sur l'estimation de cap étalonnée.
  9. Système selon l'une quelconque des revendications 7 et 8, dans lequel le ou les dispositifs de traitement sont configurés pour :
    estimer une pluralité de sous-solutions (210) pour la solution de navigation principale à l'aide d'une pluralité de sous-filtres à partir d'une séparation de solution ;
    calculer une covariance de cap pour chacune de la pluralité de sous-solutions ;
    calculer une covariance de cap pour la solution de navigation principale ;
    calculer une covariance de cap pour le filtre d'étalonnage magnétique ;
    approximer une pluralité de covariances de cap de sous-solution (212) correspondant au filtre d'étalonnage magnétique en fonction de la covariance de cap pour la solution de navigation principale, de la covariance de cap pour chacune de la pluralité de sous-solutions et de la covariance de cap pour le filtre d'étalonnage magnétique ; et
    déterminer une limite de protection (214) qui borne l'erreur sur un cap de la solution de navigation principale en fonction de séparations respectives entre la covariance de cap pour le filtre d'étalonnage magnétique et chacune des covariances de cap de sous-solution correspondant au filtre d'étalonnage magnétique.
  10. Système selon la revendication 9, dans lequel l'approximation de la pluralité de covariances de cap de sous-solution (212) correspondant au filtre d'étalonnage magnétique comporte l'approximation de la covariance de cap de sous-solution n, Cov(ψ) n,3-D , selon Cov ψ n , 3 − D ≈ γ ovrb 2 Cov ψ n , 3 − D Cov ψ 0 , DMHA Cov ψ n , DMHA
    Figure imgb0078
     où γovrb représente un facteur de bornage conservateur supérieur ou égal à un, Cov(ψ) 0,3-D représente la covariance de cap du filtre d'étalonnage magnétique, Cov(ψ)0,DMHA représente la covariance de cap du filtre de navigation principal et Cov(ψ) n,DMHA représente la covariance de cap de la sous-solution n pour le filtre de navigation principal.
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